negative integers. The plus signs represent gain(of order) and not positive
integers. And, the zeroes represent states of no change (of order), rather than an
integer with no content. Or, in the language of games: Lose, Win, or Draw.

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Thus we find that the three general classes of relationship: Net Synergy, Net

Now if we are to depict what occurs as a result of the relationship between X and Y, we
need a initial reference device. Recall our initial vectors:

X

Y

+

=

Co-Action
Vector

We can also represent our initial conditions as by the area of circles.

Y

X

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Then if we geometrically sum our circles, we get the “Initial co-Action Circle” whose
area represents the initial state of the “union” Xand Yas a “single” system.

Y

X

+

=

Initial
Co-Action
Circle
X + Y

It was considered a stroke of genius on Haskell’s part to use this Initial Co-Action
Circle
as the fourth axis of the Periodic Coordinate System. This circle represents the
state of the union at the beginning of a relationship. It is the geometric sum of (X) and
(Y) at the initiation of their co-Action. This reference circle is made by sweeping a
neutral Co-Action vector, ro, around the ORIGIN.

Y

X

(+,+)

(-,+)

(-,-)

(+,-)

(0, +)

(0, -)

(-,0)

(+,0)

(0,0)

ro

How do you represent whether or not a relationshipor co-Actionhas a synergicor
net (+) positiveeffect (increase in order), an adversaryor net (-) negativeeffect
(decrease in order), or a neutral (0)or no effect at all (no change in order) . You
must have a reference, what was the state of the system before before the co-Actionis
initiated — the condition of the individuals before their relationshipbegins. This is

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the role of the third axis — the(0, 0) circle.

Haskell sometimes called this the “scalar zero circle”, sometimes the Circle of Atropy.
Perhaps an even better name might be the Circle of Neutrality. This circle represents
a net neutralrelationship between (X) & (Y). But, regardless what we call it, the area
of this zero-zero circlerepresents the geometric sum of Xand Y’s condition at the
start of the relationship. This represents the simple sum of their individual order
before their interaction.

Finally, Haskell added a fourth axis to the Periodic Coordinate System. Along this axis
at any point, the magnitudes of (X) and (Y) are equal but their signs are opposite so the
net co-Action is zero. He called this the Axis of Atropy.

Y

X

(+,+)

(-,+)(0, +)syntropy

(-,-)

(+,-)

(0, -)

(-,0)

(+,0)

(0,0)

Axis of Atropy

entropy

Co-Action vectors which are greaterthan the radius of the zero-zero circle are net
synergic
(increasing order). Those co-Action vectors that are equalto the radius of
the zero-zero circle are net neutral (static order). And, those co-Action vectors that
arelessthan the radius of the zero-zero circle are net adversary (decreasing order).

Notice that syntropicand entropicprocess are separated by the "Axis of Atropy".
That which is to the right and up from the axis of atropy is net synergic. That which
is left and below the axis of atropy is net adversary. And that which falls on the axis

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of atropy is net neutral.

Y

X

(+,+)

(-,+)

(-,-)

(+,-)

(0, +)

(0, -)

(-,0)

(+,0)

(0,0)

Net
Synergy

Net

Net
Neutrality

This then completes the four axes of Haskells’ Periodic Coordinate System. We are now
ready to use the PCS to examine some relationships. Again recall our initial vectors:

X

Y

+

=

Co-Action
Vector

In geometry, a vector is a line whose length represents a particular quantity. The
arrow tip is used when the direction of the vector also has special meaning. In the
Periodic Coordinate Systemvectors are used to represent orderwhich has both
quantity and quality. The condition of an individual has both quantity and
quality.The direction of the vectors will be discussed later. For now, we can then sum
our vectors and examine the net effect without concern for direction.

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Now this geometric summing can produce a co-Action vector that is synergic or net
positive (increasing order).

X

Y

+

=

Or, it can produce a co-Action vector that is neutral with no net change (static order).

X

Y

+

=

No Change
Neutral

Or, it can produce a co-Action vector that is adversary or net negative (decreasing
order).

X

Y

+

=

Net Negative

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Representing our initial conditions as circles:

Y

X

+

=

( X+ Y)
Net Positive
Synergic

Y

X

+

=

(X+ Y)
No Change
Neutral

Y

X

+

=

(X+ Y)
Net Negative